Details

Time bar (total: 14.5s)

sample68.0ms

Algorithm
intervals
Results
20.0ms42×body1280valid
13.0ms139×body80valid
13.0ms34×body640valid
8.0ms30×body320valid
2.0ms11×body160valid

simplify401.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.6b

localize14.0ms

Local error

Found 3 expressions with local error:

3.6b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0b
(/ (+ x 1) (- x 1))
0.0b
(/ x (+ x 1))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
110×*-un-lft-identity
60×times-frac
57×add-sqr-sqrt
25×add-cube-cbrt
20×distribute-lft-out
18×distribute-lft-out--
14×difference-of-squares
11×associate-/r*
7×add-cbrt-cube add-exp-log associate-/l*
5×difference-of-sqr-1 add-log-exp
4×associate-/r/
3×pow1 insert-posit16
2×cbrt-undiv clear-num frac-2neg flip3-+ flip3-- div-exp flip-+ div-inv flip-- associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 117
Calls
3 calls:
Slowest
41.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
26.0ms
(/ (+ x 1) (- x 1))
13.0ms
(/ x (+ x 1))

series181.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
110.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
34.0ms
(/ x (+ x 1))
34.0ms
(/ (+ x 1) (- x 1))

simplify906.0ms

Counts
126 → 126

prune940.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

3.6b
(- (* (/ x (+ x 1)) (/ x (+ x 1))) (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))))
0.0b
(/ (- (* (/ x (+ x 1)) (/ x (+ x 1))) (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1)))) (+ (/ x (+ x 1)) (/ (+ x 1) (- x 1))))
0.0b
(+ (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0b
(* (/ x (+ x 1)) (/ x (+ x 1)))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
376×*-un-lft-identity
208×times-frac
120×distribute-lft-out
70×add-sqr-sqrt
58×add-cube-cbrt
24×swap-sqr distribute-lft-out--
18×add-cbrt-cube associate-*r* associate-*l* add-exp-log frac-sub
14×difference-of-squares
13×frac-times associate-*l/ associate-*r/
12×associate-/r*
11×pow1 associate-/r/ associate-/l/
8×add-log-exp
6×flip3-+ flip-+
5×cbrt-undiv div-exp div-inv
4×prod-exp cbrt-unprod insert-posit16 associate-/l* unswap-sqr
2×flip3-- frac-add flip--
1×pow2 +-commutative clear-num sum-log sub-neg frac-2neg pow-plus diff-log div-sub pow-prod-down pow-sqr *-commutative pow-prod-up
Counts
4 → 226
Calls
4 calls:
Slowest
94.0ms
(/ (- (* (/ x (+ x 1)) (/ x (+ x 1))) (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1)))) (+ (/ x (+ x 1)) (/ (+ x 1) (- x 1))))
35.0ms
(+ (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
28.0ms
(* (/ x (+ x 1)) (/ x (+ x 1)))
14.0ms
(- (* (/ x (+ x 1)) (/ x (+ x 1))) (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))))

series516.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
273.0ms
(/ (- (* (/ x (+ x 1)) (/ x (+ x 1))) (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1)))) (+ (/ x (+ x 1)) (/ (+ x 1) (- x 1))))
146.0ms
(- (* (/ x (+ x 1)) (/ x (+ x 1))) (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))))
60.0ms
(+ (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
38.0ms
(* (/ x (+ x 1)) (/ x (+ x 1)))

simplify1.3s

Counts
238 → 238

prune1.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

3.6b
(- (* (/ x (+ x 1)) (/ x (+ x 1))) (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))))
0.5b
(cbrt (+ (/ x (+ x 1)) (/ (+ x 1) (- x 1))))
0.5b
(cbrt (+ (/ x (+ x 1)) (/ (+ x 1) (- x 1))))
0.5b
(cbrt (+ (/ x (+ x 1)) (/ (+ x 1) (- x 1))))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
145×*-un-lft-identity
51×distribute-lft-out
48×times-frac
36×cbrt-prod
12×distribute-lft-out--
9×cbrt-div frac-sub
7×add-sqr-sqrt add-cube-cbrt
6×frac-times associate-*l/ associate-*r/ add-log-exp
4×pow1 add-cbrt-cube add-exp-log insert-posit16
3×flip3-+ pow1/3 frac-add flip-+
1×sub-neg flip3-- diff-log flip-- difference-of-squares
Counts
4 → 95
Calls
4 calls:
Slowest
28.0ms
(cbrt (+ (/ x (+ x 1)) (/ (+ x 1) (- x 1))))
26.0ms
(cbrt (+ (/ x (+ x 1)) (/ (+ x 1) (- x 1))))
25.0ms
(cbrt (+ (/ x (+ x 1)) (/ (+ x 1) (- x 1))))
14.0ms
(- (* (/ x (+ x 1)) (/ x (+ x 1))) (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))))

series482.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
134.0ms
(cbrt (+ (/ x (+ x 1)) (/ (+ x 1) (- x 1))))
129.0ms
(- (* (/ x (+ x 1)) (/ x (+ x 1))) (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))))
111.0ms
(cbrt (+ (/ x (+ x 1)) (/ (+ x 1) (- x 1))))
107.0ms
(cbrt (+ (/ x (+ x 1)) (/ (+ x 1) (- x 1))))

simplify1.4s

Counts
107 → 107

prune943.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

3.6b
(log (exp (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
3.6b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0b
(/ (+ x 1) (- x 1))
0.0b
(/ x (+ x 1))

rewrite253.0ms

Algorithm
rewrite-expression-head
Rules
159×*-un-lft-identity
80×times-frac
72×add-sqr-sqrt
31×distribute-lft-out--
28×add-cube-cbrt distribute-lft-out
18×difference-of-squares
17×log-pow
16×exp-prod
11×associate-/r*
8×add-cbrt-cube add-exp-log
7×associate-/l*
6×add-log-exp
5×pow1 log-prod difference-of-sqr-1
4×associate-/r/ insert-posit16
2×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ flip3-- div-exp exp-sum flip-+ div-inv flip-- associate-/l/
1×log-div exp-diff diff-log rem-log-exp frac-sub
Counts
4 → 149
Calls
4 calls:
Slowest
158.0ms
(log (exp (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
58.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
18.0ms
(/ (+ x 1) (- x 1))
14.0ms
(/ x (+ x 1))

series252.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
115.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
82.0ms
(log (exp (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
27.0ms
(/ (+ x 1) (- x 1))
26.0ms
(/ x (+ x 1))

simplify1.3s

Counts
161 → 161

prune1.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes87.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.7b

bsearch191.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
944.0ms1784×body1280valid
393.0ms1184×body640valid
342.0ms4048×body80valid
151.0ms649×body320valid
72.0ms335×body160valid